How Is Velocity Calculated for a 5kg Block in a Pulley System with a Spring?

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The velocity of a 5 kg block in a pulley system with a spring constant of k=40 is calculated using the tension in the system and the extensions caused by both the 5 kg and 2 kg blocks. The derived equations indicate that the total extension, represented as x1 + x2, equals 7/4. However, the correct velocity of the 5 kg block, when the 2 kg block moves upward, is definitively 1.414 m/s, which corresponds to the square root of 2.

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1. A pulley has a massless in extensible thread whose one side has a 5 kg block along with a spring of k=40 with it and the other end has a 2kg block (which is on the ground ). Find velocity of the 5kg block when the 2 kg block moves up.

The Equations part :
taking Tension as T , and extension cause by 5kg block as x1 and 2kg block as x2
we have:
T-kx1-50=Kx2-T+20


That includes my attempt as well.
I could find out the x1+x2 = 7/4 but then the velocity with that comes around as 3.45 m/s , but the correct answer is 1.414 m/s <2^1/2>.
 
Last edited:
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You seem two have omitted sections two and three from the homework template.
 

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